Self-Organized Vegetation Patterning as a Fingerprint of Climate and Human Impact on Semi-Arid...

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Self-Organized Vegetation Patterning as a Fingerprint of Climate and Human Impact on Semi-Arid EcosystemsAuthor(s): Nicolas Barbier, Pierre Couteron, Jean Lejoly, Vincent Deblauwe, Olivier LejeuneReviewed work(s):Source: Journal of Ecology, Vol. 94, No. 3 (May, 2006), pp. 537-547Published by: British Ecological SocietyStable URL: http://www.jstor.org/stable/3879600.

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2/12

Journal

of

Ecology

2006

94,

537-547

Self-organized vegetation

patterning

as a

fingerprint

of

climate and human

impact

on

semi-arid

ecosystems

NICOLAS

BARBIER,

PIERRE

COUTERON*,

JEAN

LEJOLY,

VINCENT

DEBLAUWEt

and

OLIVIER

LEJEUNEt

Universite

Libre de

Bruxelles,

Service de

Botanique

Systimatique

et

Phytosociologie,

and

tLaboratoire

d'Ecologie

du

Paysage,

CP

169,

B-1050

Bruxelles,Belgium,

Institut

rangais

e

Pondichery,

1

Saint

Louis

Street,

Pondicherry

605001,

ndia/UMR

otanique

t

bioinformatique

e

l'Architecture

es

Plantes

AMAP),

Boulevardela

Lironde,

TA401PS2,

34398

Montpellier

Cedex

05,

France,

and

$

The SIMBIOS

Centre,

Division

of

Mathematics,

University

of

Dundee,

undee

DI

4HN,

UK

Universite

ibre e

Bruxelles,

aculte

es

Sciences,

P231,

B-1050

Bruxelles,

elgium

Summary

1

Spatially

periodic

vegetation patterns

are

well

known

in

arid

and

semi-arid

regions

around the world.

2

Mathematical models have been

developed

that

attribute

this

phenomenon

to a

symmetry-breaking

instability.

Such

models

are

based on the

interplay

between com-

petitive

and

facilitative influences

that the

vegetation

exerts

on

its own

dynamics

when

it is constrained

by

arid

conditions,

but evidence for these

predictions

is still

lacking.

Moreover,

not

all

models can

account

for the

development

of

regularly

spaced

spots

of

bare

ground

in

the absence of

a

soil

prepattern.

3 We

applied

Fourier

analysis

o

high-resolution,

remotely

sensed

data

taken at either

end

of

a

40-year

interval

in

southern

Niger.

Statistical

comparisons

based on this

textural

characterization

ave

us broad-scale

vidence

hat

the

decrease

n rainfall

overrecent

decades

in

the sub-SaharanSahel has

been

accompanied

by

a detectable

shift

from

homogeneous

vegetation

cover

to

spotted patterns

marked

by

a

spatial

requency

of about

20

cycles

km-.

4

Wood

cutting

and

grazing by

domestic

animals

have

led to a much

more marked

transition

in

unprotected

areas

than

in

a

protected

reserve.

5

Field measurementsdemonstrated

hat

the

dominant

spatial

requency

was

endogenous

rather han

reflecting

he

spatial

variation

of

anypre-existing eterogeneity

n soil

properties.

6 All

these results

support

the use

of models

that

can account

for

periodic

vegetation

patterns

without

invoking

substrate

heterogeneity

or

anisotropy,

and

provide

new

elements

for

further

developments,

refinements

and tests.

7

This

study

underlines the

potential

of

studying

vegetation

pattern

properties

for

monitoring

climatic and human

impacts

on

the

extensive

fragile

areas

bordering

hot

deserts.

Explicit

consideration

of

vegetation

self-patterning

may

also

improve

our

under-

standing

of

vegetation

and climate

interactions

in

arid

areas.

Key-words: aridity,

climate

variability,

cosystem

monitoring,

Fourier

ransform,

human

pressure,

pattern

classification,

remote

sensing,

self-organization,

symmetry-breaking

instability, vegetation patterns

Journalof Ecology (2006) 94, 537-547

doi:

10.1111/j.1365-2745.2006.01126.x

Introduction

The

existence

n

the thenBritishSomaliland f

regular,

landscape-scale atterns,

n

which dense

patches

of

vegetation

alternate

with bare

soils,

was

firstrevealed

by

aerial

photographs

aken

during

he

Second

World

War.

They

were

first described

scientifically

by

Macfadyen 1950),

whose

insight

was

that

'they

are

manifestly

within he

province

f

botany

and

ecology;

the

essential

ackground

oncerns

eomorphology

nd

meteorology;

he

causes

mustbe

investigated

yphysics

Correspondence:

Nicolas Barbier

(tel.

+32

2650 21

21;

fax

+32 2650 21

25;

e-mail

[email protected]).

?

2006 The Authors

Journal

compilation

?

2006 British

Ecological

Society


3/12

538

N Barbier et al.

and

mathematics;

and the

whole

matter must

be studied

on air

photographs'.

Striped, spotted

or

arc-shaped

pat-

ternsof

different

plant

life-forms

(grass,

shrub

and

tree)

have

since been

described in

dry

zones of

Africa,

Australia,

Mexico and the

Middle

East,

on

soils

ranging

from

sandy

and

silty

to

clayey

(Tongway

et al.

2001),

and

their

occurrence at the

transition between

tropical

savannas and

hot

deserts

suggests

aridity

as the

prob-

able

triggering

factor.

Non-formalized

explanations

of

the

phenomenon

have led

to the

assumption

that

vegetation

patches

overcome

aridity

as a result of water

sheet

flow

from

upslope

bare

ground.

Recent

modelling

studies

have

mathematically

formalized

this

theory

of water

redistribution

through

runoff

(Thiery

et

al.

1995;

Dunkerley

1997).

As

sloping

ground

s

necessary

or

resource

redistribution,

and thus

for

pattern

formation,

vegetation

stripes

always develop

along

elevation

contours,

and

soil

heterogeneity

has been

called on to

explain

the

existence of

regularly spaced

bare

spots

on

nearly

flat

territory (Klausmeier

1999).

By

contrast,

another class of

models

is able to

generate

spots and stripeseven in strictlyhomogeneous and iso-

tropic

(non-sloping)

environments

(Lefever

&

Lejeune

1997;

von

Hardenberg

et al.

2001;

HilleRisLambers

et al.

2001;

Okayazu

&

Aizawa

2001).

The

pattern

is

generated

by

an

instability

that leads

to the

disruption

of

spatial

symmetry:

the

approach

is

derived

from

the

seminal

work of

Turing

1952),

which

has

already nspired

many

applications

in

physics, chemistry

and

biology

(Cross

&

Hohenberg

1993;

Murray

2003).

The

slope-

induced

anisotropy,

f

present,

s then

merely nterpreted

as

a

secondary

factor

that

leads to the

formation of

stripes

rather than

spots,

and

potentially

drives the

progressive

motion

of

the

pattern.

Thegeneralcontributionof mathematicalmodelling

has been

to show

that

nteractions

between

plants

at

scales

of

the

order of

a fewmetres

may

result in the

emergence

of

spatially periodic

distributions of

vegetation having

wavelengths

(i.e.

the

distance between

two

consecutive

highs

or

lows in

vegetation

density)

in the orderof tens

or

hundreds

of

metres. It can

be

demonstrated that all

these

models of

vegetation

dynamics

involve the inter-

play

of

competitive

effects

related o soil

water

consump-

tion

and facilitative

effects

resulting

from

soil water

budget

enhancement

by vegetation.

For

pattern

ormation

to

occur,

negative

interactions

(competition)

must have

a

larger

range

than

positive

interactions

(facilitation),

analogous

to the

well-known condition of

short-range

activation

and

long-range

nhibition n

reaction-diffusion

systems Nicolis

&

Prigogine 1977).

Moreover,

all models

agree

that

patterning

occurs when

vegetation growth

decreases,

for

instance

as

a

result of

reduced

water

availability,

nd

therefore iew

patterns

as

a

self-organized

response

of

vegetation

o resource

carcity Lejeune

et al.

2002). However,

different

classes of models

predict

dis-

tinct

patterning

cenarios

below acritical

aridity

hreshold.

In

the absence of

prepatterning

n substrate

properties,

slope-based

models

always

show

a transition rom homo-

geneous

to

striped vegetation,

whereas

the second class

consistently

shows

a shift from

homogeneous

cover

to

vegetation punctuated

by

bare

spots.

The

distribution

of bare

spots

is

spatially periodic

and

displays

a

clear

dominant

spatial frequency (i.e.

the number

of

repeti-

tions of the

pattern

within

a

given

window;

the

inverse

of the

wavelength)

n Fourier

space

(Lejeune

et al.

1999;

Couteron

&

Lejeune

2001).

In

simulations,

as

aridity

increases

further,

bare

spots merge

into

'labyrinthine'

stripes,

which

subsequently

become

a bare matrix

sur-

rounding

spots

of

vegetation

that

eventually disappear

and leave

a

complete

desert.

The

main

purpose

of this

paper

is to

provide

broad-

scale

empirical

evidence for

the

emergence

of

self-

organizedpatterns

of bare

spots

in

response

o increased

aridity.

A

general

trend towards

ower

rainfall,

observed

across

the African Sahel

during

the second

half of

the

last

century

(Nicholson

2001;

IPCC

2001),

allowed

us

to

monitor

changes

in the

spatial

distributionof

vege-

tation. Our

study

area in south-west

Niger

is located

at

the wetter end of the climatic

range

in which

periodic

patterns

are

presently

observed in subsaharan

West

Africa(Couteron&Lejeune2001)andencompassesboth

a

protected

area,

experiencingonly

rainfall

decrease,

and

adjacent,unprotected

areas

subjected

to both

decreas-

ing

rainfall and

increasing

human

pressure.

Extensive

remote

sensing

data taken over a

period

of 40

years,

coupled

with intensive

field

measurements,

allow us

to

address the

following

questions.

(i)

Can decreased

rain-

fall drive the

emergence

of

spatially periodic spots

of

bare

ground

- i.e.

spotted patterns

- in

vegetation,

all

other

things being

equal?

(ii)

If

so,

is the

phenomenon

intrinsic to

plant

population

dynamics

or does it

reveal

pre-existing

soil

heterogeneity?

iii)

What

is the

relative

influence

of climatic

and

anthropogenic

factors on

the

process?

Materials and methods

STUDY AREA

Our

investigations

were carried

out in south-west

Niger

at the southern

(and

wettest)

extremity

of a

latitudinal

climatic

gradient

between 12'N and

15'N

(1951-89

average

annual rainfall

ranges

from 700 mm to 300

mm;

L'H6te

&

Mah6

1996).

Periodic

patterns

of

alternating

bare

ground

and dense

vegetation

are

systematically

observed all

along

the

gradient

on

iron-capped

plateaus,

with

spotted patterns being predominant

in the

south

and

banding

in the northern stretches. In West

Africa,

such

patterns

are

formed

by

dense thicketsof tall

shrubs

(especially

CombretummicranthumG.

Don),

in

associ-

ation with annual

grasses (Couteron

&

Lejeune 2001).

South

of

12?N,

periodicpatterns

are no

longer observ-

able,

even on

iron-capped plateaus,

and the

vegetation

cover,

which no

longer displays regular patches

of bare

soil,

can be describedas a tree

savanna,

with mixed cover

of both tall

perennial

and

annual

grasses

associated

with scattered trees and shrubs.

Dry

season

fires,

which

are

regular

events in these

savannas,

rarely

affect

spotted

C

2006

The

Authors

Journal

ompilation

C

2006 British

Ecological

Society,

Journal

of

Ecology,

94,

537-547


4/12

539

Self-organized

vegetation

patterning

Fig.

1

Typical pottedpattern

bare

oil s

lightcoloured)

nd ield

tudy

et

up:perspective blique

iew

showing

ransects

three

50-m

transects or

soil

survey,

one

250-m

transect or

vegetation-relief

orrelation

tudy)

and a

120-m

by

70-m

area for

topographical

mapping.

vegetation

due

to both the lower

quantity

and the

frag-

mented distribution

of

ignitable

herbaceous biomass.

The influence of

drought

on

vegetation

pattern

for-

mation was addressedby monitoring vegetation change

in a

protected

area

(Niger part

of

theW

Trans

boundary

Biosphere

Reserve

-

12'14'-12'30'

N,

2'14'-2?45'

E)

while the combined influences of

drought

and human

activities were considered

by monitoring

the immediate

surroundings

on the

opposite

(east)

bank of the River

Niger

(district

of

Birnin

Gaoure).

In the

reserve,

as well

as

in the

surrounding

districts,

extensive areas of

peri-

odic

spotted vegetation patterns (Fig.

1)

are

presently

observed on

iron-cappedplateaus,

which are more xeric

than other

topographic positions.

Officialstatisticsfor

the district of

Birnin

Gaoure

give

a human

density

of

50 inhabitants

km-2with

a

demographic

annual

growth

rate of around 4%over the last decade. Except for the

reserve,

he whole

region

of south-west

Niger

is,

in

fact,

characterized

by

a human

population (density

>

20

km-2

and

growth

rate

>

3%;

Raynaut 2001)

that is

compar-

atively

denser and is

expanding

faster than the African

Sahel

average.

On

iron-capped plateaus,

neither

crops

nor settlements

are

generally

observed and human

pressure

is

mostly

exerted via

wood-cutting

and

graz-

ing

of domestic

herds,

which both result in a diffuse

suppression

of

plant

biomass. Since establishment

in

1954,

the reservehas

been

kept

free from

major

human

influences,

except

for the limited

poaching

of

wildlife

and brief

night crossing

of domestic

herds

(Leberre

&

Messan 1995).

The local

rainfall series

(Fig. 2)

shows the difference

between the

years

before the late 1960s

(1921-68),

with

average

ainfallof 670

mm

yr-',

and the

subsequentyears,

characterized

y

both lower

average

ainfall

550

mm

yr-')

and

limited,

but

severe,

drought

periods, particularly

n

the

early

1970s and 1980s.

There is a

regular

atitudinal

gradient

n

average

rainfallof

approximately

1

mm

yr-'

for

each kilometre northwards

(L'H6te

& Mahe

1996),

and similar variation was

found for locations in and

around he

study

area

series

of

Say,

Tamou,

La

Tapoa

and

Kandi;

datanot

shown).

The

study set-up

was orientated

1920 1930 1940 1950 1960

1970 1980 1990 2000

350

250

150

-50

S-150-

r

-250-

-350

Year

Fig.

2

Rainfall data for 1921-2002 at the

meteorological

stationof

Say (source:

Direction

Met6orologique

ationale,

Niger)

xpressed

s annual ariation

bars)

round he

nterval

mean

(619.5mm).

The continuous

ine shows the

moving

average

f the five

preceding

ears.

longitudinally,

with

protected

and

unprotected

sites at

similar

latitude to avoid the

effects of this

gradient.

REMOTELYSENSED

DATA

Diachronic aerial

photographs

were used to

survey

both

temporal

and

spatial

variation of

vegetation

patterns.

Panchromatic

ontacts

(IGN-Niger,

1

: 50

000,

December

1956 and December

1996)

were

digitized

into

greyscale

levels with a

pixel

size of

2 m

that was sufficient

to

study

decametric-scale

patterns.

Tests with

higher

resolution,

i.e. 1 m

pixel-'

or

less,

led to similar

results for all ana-

lyses. On the

digitized images, bright

pixels correspond

to bare

soil,

whereas dark

pixels

result from

woody

vegetation,

and intermediate

greyscale pixels

relate to

continuous

grass

cover. At

first

approximation, grey-

scale values can be considered

as a monotonic function

of

phytomass.

We

systematically

ampled

a

rectangular tudy region

of c.

100

x

30 km

(with

the

longer

dimension orientated

east-west)

via 29

square

areas of 9

km2

(total

sampling

rate of

8.7%),

about half of which

(14)

were

located

in

the

park.

These areas were

sampled

according

to a

10-km

by

10-km

grid,

with some local

adjustments

to

?

2006

The Authors

Journal

ompilation

C

2006British

Ecological

ociety,

Journal

of

Ecology,

94,

537-547


5/12

540

N Barbier et

al.

ensure that each

sample

area was found close to the

centres of a

picture

from each of the two

dates. This

allowed a

relatively precise superimposition

of 1956

and

1996

digitized

photographs

without

requesting

geometrical

corrections.

Geographical

invariants

were

found

within

each

area and

superposition

was achieved

with a root

mean

square

error of less than

4

m. The

29

areas were then subdivided into

square

windows of

300 m

on

a side. At

each

date,

2900 such windows

were

submitted to

quantitative

pattern analysis.

QUANTITATIVE

PATTERN

ANALYSIS

AND

CLASSIFICATION

We

used the two-dimensional

(2D)

Fourier transform

andthe

subsequentcomputation

of the2D

periodogram

(Mugglestone

& Renshaw

1998),

also known as the

power spectrum

in

engineering

sciences,

to

obtain

a

quantitative

characterization of the

patterns

observa-

ble

in

the

greyscale

images.

This method

is known to be

appropriate

when

spatial periodicity

is

present

in

the

signal under study, as periodogram amplitude values

directly express

the

proportions

of

image

variance that

are accounted for

by periodic

functions of

explicit spa-

tial

frequencies

and orientations. The characterization

is

independent

of the actual mean and variance of the

images, making

it a

powerful

tool to

compare images

without the need

to

request

time-consuming

radiomet-

ric

corrections

(Couteron

2002).

Our

approach

differs

from the method used

by

Ares et al.

(2003)

in that

we

computed spectra

from

2D

image

periodograms

(rather

than

1D

periodograms

rom

transects),

and we used these

spectral

values instead of a

unique signal-to-noise

ratio

to

compare

and

interpret spectra.

Two-dimensional periodograms were simplified so

as to

capture separately pattern

information relative to

spatial requency

nd to

spatial

orientation.This was done

by summing

periodogram

values on either

ring-shaped

or

wedge-shaped

concentric

frequency

regions

to com-

pute

the

r-

and

0-spectra, respectively (Mugglestone

&

Renshaw

1998;

Couteron

2002).

The

r-spectrum

xpresses

the

partition

of the

image

variance

among spatial

fre-

quencies

while the

0-spectrum

expresses

the

partition

among spatial

orientations. We

further derived a

synthetic

index of

pattern isotropy by computing

Shannon's

entropy (Legendre

&

Legendre 1998)

on the

values of the

0-spectrum.

Highly anisotropic patterns

(dominated by a particular orientation) show a unique

prominent

peak

in their

0-spectra

and a low

entropy

value.

Conversely, sotropic patterns

whose variance is

scattered

among

all orientations

(fairlyflat

0-spectrum)

should

yield high entropy figures. [The

maximum value

for a

strictly

flat

0-spectrum

would

be

2.9,

i.e.

ln(18)/18,

as we

partitioned

the

0-1800

range

into 18 direction

classes of

100.]

Pairwise

comparisons

of

r-spectra

were carried out

using

the

log-ratio technique,

which is well suited for

the

computation

of

confidence ntervals

F-distribution;

Diggle 1990).

In

Fig.

3 we illustrate the

method

by

(a)

1956 1996

0 100 200

300

0 100 200 300

metres

metres

(b)

-- 1996/1956

"

C.I.

o

0.5

0

0

a)

0

-1

0 10

20

30 40

50 60

Cycles

km-1

Fig.

3

Diachronic

comparison

of

vegetation

aspect

in a

particular

window:

a)

aerial

photographswindows

300

m

on a

side);

baresoil

appears

n white and

vegetation

n

grey

(light

to medium for

herbaceous

cover,

dark for

bushes,

thicketsand

trees). b) Log

ratio

between he

1996and 1956

Fourier

-spectra.

Dashed ines

represent

he

95% onfidence

interval

CI)

computed

under he null

hypothesis

f

absence

of

change

between1956

and 1996.

comparing

two

diachronic

versions of the same

window

(Fig. 3a).

The shiftfrom

homogeneous

savanna

o

spotted

vegetation is clearlycharacterizedby the emergenceof

a

peak

in the

r-spectrum,

while the

log-ratio

between

r-

spectra

(Fig.

3b)

shows which

spatial

frequencies

have

undergone

a

statistically significant

increase

(i.e.

those

having

values

above the

upper

confidence

envelopes).

Note

that for

generalityspatial

frequencies

are

expressed

in

cycles

km-'

rather than in

wavenumbers.

Each

temporal

version of a

window is

characterized

by

its

r-spectrum,

and can be

seen as

being

described

by

quantitative

variables

(or

'features';

Tang

& Stewart

2000),

which are the

contributions

of successive

spatial

frequencies

to

image

variance

(we

restrict

ourselves to

the first 25

wavenumbers,

.e.

spatialfrequencies

smaller

than 83 cycles km-1or wavelengthsabove 12

m).

Non-

hierarchical,

unsupervisedclustering

using

the

K-means

algorithm

and

the

Euclidean distance

(Legendre

&

Legendre 1998)

was

performed

on

the

r-spectra

table

(after

standardization,

i.e.

centring

of each

variable

by

its mean and

division

by

its

standard

deviation)

to clas-

sify

windows

objectively

nto four classes.

The two dates

(n

=

5800

windows)

were

analysed

together

in

order to

obtain acommon frameof

reference or

observingpattern

dynamics

between

the dates. We

further built

two-way

contingency

tables

between dates and

classes

in

order

to test the

significance

of

interdate

variations

in

class

C 2006

TheAuthors

Journal

ompilation

C

2006

British

Ecological

Society,

Journal

of

Ecology,

94,

537-547


6/12

541

Self-organized

vegetation

patterning

frequencies

Bishop's

criticalvalueson

Freeman-Tukey

deviates).

Finally,

we

mapped

the

categories

on the

digi-

tized aerial

photographs by superimposing categorical

symbols

at

the centre of each

300-m

sampling

window.

FIELD

MEASUREMENTS

In

order to

assess whether the

observed

periodic spatial

patterning

could derive

from

pre-existing

substratum

heterogeneities,

we

selected a

typical

spotted

vegeta-

tion

site,

located in the

middle of the

protected park,

for

intensive field

investigations

(Fig.

1).

The

vegetation,

geomorphology

and soil

properties

were characteristic

of the

iron-capped plateaus

of the whole

region,

and

the

selected site had

witnessed the

overall

emergence

of

spotted patterns

that

are

described

and

analysed

below.

Topographical

mapping

was carried out

(instrumental

error ess than

5

mm)

in

a

120-m

by

70-m

area and

along

a

250-m

transect

using

an

optical

theodolite

(Metland

MTXOTM)

nd a laser

meter

(Leica

DistoTM) adapted

on the

theodolite.

Along

the

transect,

vegetation

cover

was visually estimated in quadratsof 1 m on a side.To

evaluate the

spatial

correlation

between cover and

local

elevation

along

a

transect,

the

Fourier coherence

spec-

trum

(Diggle 1990)

was

computed

between

vegetation

cover and

detrended

elevation. This

spectrum

s

derived

from the

cross-periodogram

uilt from

the

two

processes

and is

interpreted

as a

series of correlation coefficients

(ranging

from

0 to

1)

between the

spatialfrequencies

of

the two

processes.

Envelopes

were

built from the standard

error of the

coherence

spectrum (computed following

Diggle 1990).

Other soil

parameters

such as soil

depth

above the

ironpan,

depth

of the

layer

of iron

nodules,

particle

size

(proportions in seven classes) and bulk density were

measured

from 32 soil

pits

regularly sampled every

5

m

along

three

transects

(Fig. 1).

A

two-way

ANOVA

Sokal

& Rohlf

1995), using

vegetation

cover

(either

bare

or

vegetated)

and

transects as

factors,

was

performed

to

explore

the

variability

of

soil

parameters

in relationto

the

vegetation pattern.

Spatial

dependency

between

residuals of

the ANOVAas tested

using

Young's

test

for

serial

independence.

Results

PERIODIC PATTERN AND SUBSTRATUM

VARIATION

Two-dimensional

topographical

mapping

revealed that

vegetation

was not restricted to local

depressions

(Fig. 4a),

contradicting

he idea that

spottedpatternsmay

directly

match

slightpre-existing

ubstratum

rregularities.

The

coherence

spectrum, giving

the correlation coeffi-

cients

between the

spatial frequencies

of two different

processes,

was

computed

between detrended local ele-

vation and

vegetation

cover measured

along

a transect.

This

spectrum

showed the absence of

any significant

relationship

at relevant

spatialfrequencies.

n

particular,

coherency

estimates

did

not

differ

significantly

from

zero

for

the

spatial

frequencies

of c. 20

cycles

km-1

see

below) characterizing

the

periodic vegetation

pattern

(Fig.

4b). By

contrast,

the

mapped

area

proved

not

to

be

completely

isotropic

as a

generalslope

of c. 0.6%

was

observed. It is

interesting

to note that in the central

part

of the

mapped

area,

where the

slope

was

highest (i.e.

1.7%),

the

spotted

(isotropic) pattern

of

vegetation

tended

to become

anisotropic (i.e. banded) by aligning

perpendicularly

to the

slope.

The

two-way

ANOVA

n

soil

parameters

showed that the

only

significant

differ-

ence between

bare

and

vegetated

areas was found

for

bulk

density. Although

other

parameters

whose

spatial

variation

might

be

expected

to determine

vegetation

patterns

did not show

any significant

relationship

with

vegetation

cover,

they

did show

significant

differences

between transects.

The

scale

of this

spatial variability

was

not,

however,

reflected

by

the

periodic vegetation

pattern.

Residuals of the

ANOVA

id

not

show

spatial

autocorrelation

along

transects.

CLASSIFICATION

OF LAND COVER SPATIAL

PATTERNS

We submitted

the

5800

(two

temporal

versions

of

2900

windows)

individual

standardized

r-spectra

o

K-means

clustering.

The

r-spectrum

gives

the

signature

of each

window

in

terms of

spatial frequencies,

and the

purpose

of

applying

this

clustering algorithm

was therefore to

classify

windows

on the basis

of

their resemblance

(Euclidian

distance)

with

respect

to the coarseness or

fineness

of the texture. The

resulting

four

classes

gave

a

clear

interpretation

in

terms of textural

properties

of

the windows

(Fig.

5)

and

therefore in terms of

land

cover features or vegetation types (Fig. 6). Class C1

(spotted)

was characterized

by

a

strong peak

of

the

mean standardized

r-spectrum

in

the

range

20-30

cycles

km-1,

i.e.

for

spatial

frequencies

that

were iden-

tified

by preliminary

analyses

as

characterizing

spotted

periodic

vegetation

(Fig. 3).

The

three

remaining

classes

were

ordered

along

a

textural

gradient

according

to

the

relative

importance

of small vs.

large spatial frequen-

cies

in the

r-spectrum:

C3

(macro)

was characterized

by

a

peak

in

the small

spatial frequencies

(

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